Evaluate square root of 180- square root of 125

$\sqrt{180} - \sqrt{125}$

Step 1

Simplify each term.

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$\sqrt{36 (5)} - \sqrt{125}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 5} - \sqrt{125}$

$\sqrt{6^{2} \cdot 5} - \sqrt{125}$

Pull terms out from under the radical.

$6 \sqrt{5} - \sqrt{125}$

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$6 \sqrt{5} - \sqrt{25 (5)}$

Rewrite $25$ as $5^{2}$ .

$6 \sqrt{5} - \sqrt{5^{2} \cdot 5}$

$6 \sqrt{5} - \sqrt{5^{2} \cdot 5}$

Pull terms out from under the radical.

$6 \sqrt{5} - (5 \sqrt{5})$

Multiply $5$ by $- 1$ .

$6 \sqrt{5} - 5 \sqrt{5}$

$6 \sqrt{5} - 5 \sqrt{5}$

Step 2

Subtract $5 \sqrt{5}$ from $6 \sqrt{5}$ .

$\sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$

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